Copy_of_neurons_exercises.ipynb

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        "<a href=\"https://colab.research.google.com/github/Sciterra/2nd-work/blob/master/Copy_of_neurons_exercises.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# Neuron Physiology Data Analysis Exercises"
      ]
    },
    {
      "metadata": {
        "id": "3Oz0m02JnBhy",
        "colab_type": "text"
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      "cell_type": "markdown",
      "source": [
        "### - Replace the \"...\" with code and/or values to complete each problem\n",
        "### - Always execute cells from top to bottom!"
      ]
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      "source": [
        "# Our preamble\n",
        "# Always plot in the notebook\n",
        "%matplotlib inline\n",
        "# Load the plotting library\n",
        "import matplotlib.pyplot as plt\n",
        "# Load the math library\n",
        "import numpy as np\n",
        "# Load more science stuff\n",
        "import scipy\n",
        "import scipy.constants as constants\n",
        "# Load pandas to make and manipulated data frames\n",
        "import pandas as pd\n",
        "# Load a library for nicer-looking grpahics\n",
        "import seaborn as sns\n",
        "# Nice big fonts\n",
        "sns.set(font_scale=1.5)\n",
        "# Load a library to turn warnings on and off\n",
        "import warnings\n",
        "# Turn off distracting warning messages that you don't need to see and will confuse you\n",
        "warnings.filterwarnings(\"ignore\")"
      ],
      "execution_count": 0,
      "outputs": []
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      },
      "cell_type": "code",
      "source": [
        "# Install some packages that you will need\n",
        "!pip install quantities\n",
        "# Install the quantities package for keeping track of units and dimensional analysis\n",
        "import quantities as pq"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: quantities in /usr/local/lib/python3.6/dist-packages (0.12.2)\n"
          ],
          "name": "stdout"
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      "cell_type": "markdown",
      "source": [
        "<hr>"
      ]
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      "source": [
        "## 1) "
      ]
    },
    {
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      "source": [
        "![ghk](https://raw.githubusercontent.com/rgerkin/neuro-data-analysis-course/master/images/ghk.jpg) "
      ]
    },
    {
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      "source": [
        "#### The voltage difference between the inside and oustide of the cell, the so-called \"membrane potential\", is driven by differences in ion concentrations and differences in the permeability of the membrane to those ions.  It is described by the Goldman-Hodgkin-Katz (GHK) equation:\n",
        "\n",
        "#### $$ v = \\frac{RT}{F}ln\\frac{\\sum_i{p_ic_{i[out]}}}{\\sum_i{p_ic_{i[in]}}}$$ \n",
        "\n",
        "#### where $v$ is the membrane potential, $R$ is the ideal gas constant, $T$ is the temperature in Kelvin, $F$ is Faraday's constant, $P_i$ is the membrane permeability of ion $i$ (a reflect of how many ion channels are open for it to travel through), $c_{i[in]}$ is (usually) the concentration of ion $i$ inside the cell, and $c_{i[out]}$ is the (usually) concentration of ion $i$ outside the cell.  But when ions have negative charge (e.g. $Cl^-$), \"in\" and \"out\" get swapped, because the ion (negative) and the current (positive, by convention) flow in opposite directions.  "
      ]
    },
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      "source": [
        "#### Use the GHK equation to determinethe membrane potential at 310 degrees Kelvin (37 degrees Celsius, i.e. human body temperature) for the figure above, assuming that $P_{Na} = 0.05$, $P_K = 1$ , and $P_{Cl} = 0.45$"
      ]
    },
    {
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      "cell_type": "markdown",
      "source": [
        "#### 1a)"
      ]
    },
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      "source": [
        "# Change this to the correct temperature in Kelvin, but keep the attached units\n",
        "T = 310* pq.K\n",
        "\n",
        "# These already have the correct values\n",
        "R  = constants.R * pq.J / (pq.mol * pq.K)\n",
        "F = constants.physical_constants['Faraday constant'][0] * pq.C / pq.mol\n",
        "\n",
        "# These permeabilties have the \"correct\" values above\n",
        "P = np.array([0.05, 1, 0.45]) / pq.mM # Permeabilities \n",
        "\n",
        "# Put the correct intracellular values in from the figure above (Na, K, Ca).  \n",
        "C_in = np.array([10, 148, 103]) * pq.mM\n",
        "\n",
        "# Put the correct extracellular values in from the figure above.  \n",
        "C_out = np.array([142, 5, 4]) * pq.mM"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
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      "cell_type": "markdown",
      "source": [
        "#### 1b)"
      ]
    },
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      "cell_type": "code",
      "source": [
        "# A sum of products can be implemented as a product of arrays in Python.  \n",
        "# For example:  \n",
        "x = np.array([1, 2, 3])\n",
        "y = np.array([4, 5, 6])\n",
        "np.sum(x*y) # This will add 1*4, 2*5, and 3*6\n",
        "\n",
        "# Use this technique to create the numerator and denominator of the term inside the `ln` in the GHK equation:  \n",
        "numerator = np.sum(P*C_out) # This is the sum of P*C_out for each ion \n",
        "denominator = np.sum(P*C_in) # This is the sum of P*C_in for each ion\n",
        "\n",
        "# Finally, we compute the membrane potential v from all of these pieces.  Note that `log` is the natural logarithm (ln) in Python.  \n",
        "V = (R*T/F) * np.log(numerator / denominator)\n",
        "\n",
        "# Print the result (units will look weird, don't worry)\n",
        "V"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array(-0.07053335) * J/C"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
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      "source": [
        "#### 1c) These units look strange, but maybe they are equivalent to voltage, in the same way that \"furlongs per fortnight\" is equivalent to speed. If so, we can \"rescale\" to our desired units of $mV$ (hint: it should be near $-70 mV$):"
      ]
    },
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        "outputId": "34f77b05-e263-4407-9748-9f2c9b2460e7",
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      "cell_type": "code",
      "source": [
        "V.rescale(pq.mV)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array(-70.53334545) * mV"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
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      "cell_type": "markdown",
      "source": [
        "#### 1d) And print the result to 3 significant digits:"
      ]
    },
    {
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      "cell_type": "code",
      "source": [
        "print(\"The membrane potential is %.3g mV.\" % V.rescale(pq.mV))"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The membrane potential is -70.5 mV.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "owdLrcyanBih",
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      "cell_type": "markdown",
      "source": [
        "#### 1e) The proud owner of this neuron ate too many bananas, and all of his potassium regulatory mechanisms aren't working.  His extracellular potassium shot up by an additional 10 mM.  What happens to the resting potential of this neuron?  Will this make this cell more or less active?"
      ]
    },
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      "source": [
        "# Put the correct extracellular values in from the figure above.  \n",
        "C_out = [142, 15, 4] * pq.mM\n",
        "numerator = np.sum(P*C_out) # This is the sum of P*C_out for each ion \n",
        "V = (R*T/F) * np.log(numerator / denominator)\n",
        "print(\"The membrane potential is %.3g mV.\" % V.rescale(pq.mV))\n",
        "print(V)\n",
        "print(\"Higher\")\n"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The membrane potential is -56.1 mV.\n",
            "-0.056054784448581994 J/C\n",
            "Higher\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
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      "cell_type": "markdown",
      "source": [
        "<hr>"
      ]
    },
    {
      "metadata": {
        "id": "dMKg-UOZnBin",
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      "cell_type": "markdown",
      "source": [
        "## 2)  "
      ]
    },
    {
      "metadata": {
        "id": "4OZnfezJnBio",
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      },
      "cell_type": "markdown",
      "source": [
        "![threshold](https://slideplayer.com/slide/4667714/15/images/6/Action+potential.jpg)"
      ]
    },
    {
      "metadata": {
        "id": "ezfO5pS0nBiq",
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      "cell_type": "markdown",
      "source": [
        "#### Neurons initiate action potentials as a result of positive feedback: first, sodium enters the cell, raising the membrane potential; then, voltage-dependent sodium channels open in response to this change, and let even more sodium in.  The \"point of no return\" for this process is called the neuron's ***threshold***, and occurs when this positive feedback will continue even in the absence of any additional input to the cell, causing an action potential.  "
      ]
    },
    {
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        "id": "kTjkK1IInBir",
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      },
      "cell_type": "code",
      "source": [
        "# Load data form the Allen Institute, saved from the previous lecture\n",
        "url = \"https://raw.githubusercontent.com/rgerkin/neuro-data-analysis-course/master/data/sample_trace.csv\"\n",
        "df = pd.read_csv(url, index_col=0) # index_col=0 means that the first column (time) should be the index\n",
        "\n",
        "# Plot the cell's response (from the data frame column 'response') to the stimulus (not shown, but in column 'stimulus'), on a 12x3 canvas\n",
        "df.plot(y='response', figsize=(12,3));\n",
        "\n",
        "# Zoom the x-axis in to the interesting part, starting just before and ending just after the stimulus.  Label the axes.\n",
        "plt.xlim(0.9, 2.1);\n",
        "plt.xlabel('Time (s)')\n",
        "plt.ylabel('Membrane\\nPotential (mV)');"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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wd+5c3H777XEJHS8qKysBICqkp6ioCBUVFbZpi4pykZ6eJk22VEBJSb5QuuaW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\nhx/GTTfdhLVr16K+vh6FhYU48sgjHUNxXKQ+nOLMtPi/bp3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89Q4YB1xb/EHTYjz5gqPM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\n",
            "text/plain": [
              "<Figure size 864x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "BOEg8as2nBiw",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### 2a) How many action potentials (spikes) occurred in response to this stimulus?  Hint: use the example from the most recent lecture if you don't know how to count the number of elements in an array"
      ]
    },
    {
      "metadata": {
        "id": "ETeEM7xknBix",
        "colab_type": "code",
        "outputId": "d84eb057-b522-4340-fc20-dbc8fac11449",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "cell_type": "code",
      "source": [
        "# Import the function for peak finding.\n",
        "from scipy.signal import find_peaks\n",
        "\n",
        "# Find the peak locations and heights, for peaks that go above 0\n",
        "spike_times, spike_amplitudes = find_peaks(df['response'], height=0)\n",
        "\n",
        "n_spikes = len(spike_times)\n",
        "\n",
        "# Write a print statement (as in question #1) that says how many spikes there were.\n",
        "# Hint: %d will print a value as an integer. \n",
        "print((\"number of spikes is %.3g.\" % n_spikes))"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "number of spikes is 49.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "UrKaADeMnBi1",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### There are many ways to define the threshold, but says that the threshold is when the slope of the membrane potential (the response shown above) suddenly becomes very positive.  "
      ]
    },
    {
      "metadata": {
        "id": "_CEgobG2nBi2",
        "colab_type": "code",
        "outputId": "cc02355e-4eea-42a6-fa95-42efc9068f9e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 235
        }
      },
      "cell_type": "code",
      "source": [
        "# Plot the cell's response (from the data frame column 'response') to the stimulus (not shown, but in column 'stimulus'), on a 12x3 canvas\n",
        "df.plot(y='response', figsize=(12,3));\n",
        "\n",
        "# Zoom the x-axis in to the interesting part, starting just before and ending just after the stimulus\n",
        "plt.xlim(1.02, 1.05);\n",
        "plt.xlabel('Time (s)')\n",
        "plt.ylabel('Membrane\\nPotential (mV)');"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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rbW3F999/j3nz5qG4uLjbXIM1a9b067XDxefz8fTTTw+JwIQQEprAyoAwpJWB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\nTAaIiIiIiAIUkwEiIiIiogD1/wHu1jjpUimISwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "kVAiYh-_nBi8",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### See the event right at (or just before) t = 1.030 seconds?  That is a good example of a threshold (the slope suddenly became very positive). You may recall that the slope is equal to the first derivative (with respect to time).  "
      ]
    },
    {
      "metadata": {
        "id": "XMfQnAQCnBjH",
        "colab_type": "code",
        "outputId": "d5f09b0a-a48f-4f14-cede-890ff2d7689f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 235
        }
      },
      "cell_type": "code",
      "source": [
        "# Compute the first difference (the difference between adjacent samples of the membrane potential)\n",
        "# This will be in units of \"mV\" (millivolts)\n",
        "dv = df['response'].diff() * pq.mV\n",
        "\n",
        "# Compute the time step (the difference in time from one sample to the next)\n",
        "# This value is the same for all adjacent time samples, so we can just pick the first two\n",
        "# This will be in units of \"s\" (seconds)\n",
        "dt = (df.index[1] - df.index[0]) * pq.s\n",
        "\n",
        "# Let's use \"ms\" (milliseconds) instead because it will be more graphically intuitive\n",
        "dt = dt.rescale('ms')\n",
        "\n",
        "# The first derivative with respect to time is dv/dt.  \n",
        "# Python doesn't allow us to put the \"/\" sign in a variable name, so we won't.  \n",
        "# This will have units of \"mV/ms\"\n",
        "dvdt = dv/dt\n",
        "\n",
        "dvdt.plot(figsize=(12,3))\n",
        "\n",
        "# Zoom the x-axis in to the interesting part, starting just before and ending just after the stimulus\n",
        "plt.xlim(1.02, 1.05);\n",
        "plt.xlabel('Time (s)')\n",
        "plt.ylabel('First derivative\\nof membrane\\npotential (mV/s)');\n",
        "\n",
        "# Add a red dotted line at dv/dt = 20 mV/ms\n",
        "plt.plot([0,2],[20,20],'--r');"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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+fn4sWbKkyp1UFVT079+/3M9FRUU88MAD6HQ6/P39KS4uxmw24+fnx9/+9rdK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\nGFQQEREREZFO/j+K+KrcsJ1WXAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "Rhrmaz31nBjM",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### I've put a red line there to indicate when the slope (dv/dt, shown above) of the original trace (v, shown in the previous figure) gets significantly higher than the baseline. We can call the times when the dv/dt first exceeds this red line, for each spike, the spikes' thresholds.  "
      ]
    },
    {
      "metadata": {
        "id": "5pWQS01LnBjM",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### 2b) Extract all the values from the original dataframe when dv/dt exceeds the value shown in the red line (20 mV/ms)"
      ]
    },
    {
      "metadata": {
        "id": "aMutQHMgnBjQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 622
        },
        "outputId": "60c6d87d-74a9-4943-c887-7e6f32d9876d"
      },
      "cell_type": "code",
      "source": [
        "# You can add a column to any dataframe by just assigning to it with the equals sign.  \n",
        "# This will give you a new column containing the first derivative that we computed above.  \n",
        "df[\"derivative\"] = dvdt\n",
        "\n",
        "# Do you remember how we create a selector (with the double equals sign)?\n",
        "# You don't have use ==, as you can use >, <, >=, <= or any other comparison operation you can think of.\n",
        "is_slope_greater_than_threshold = (df[\"derivative\"] > 20)\n",
        "\n",
        "# Now do the extraction:  \n",
        "places_where_slope_is_greater_than_threshold = df[is_slope_greater_than_threshold]\n",
        "\n",
        "# Show the first rew rows\n",
        "places_where_slope_is_greater_than_threshold.head(20)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>stimulus</th>\n",
              "      <th>response</th>\n",
              "      <th>derivative</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1.02992</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-38.2188</td>\n",
              "      <td>20.310</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.02994</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-37.5313</td>\n",
              "      <td>34.375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.02996</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-36.1250</td>\n",
              "      <td>70.315</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.02998</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-33.7500</td>\n",
              "      <td>118.750</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03000</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-30.6875</td>\n",
              "      <td>153.125</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03002</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-27.0625</td>\n",
              "      <td>181.250</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03004</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-23.0938</td>\n",
              "      <td>198.435</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03006</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-18.0312</td>\n",
              "      <td>253.130</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03008</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-11.5938</td>\n",
              "      <td>321.870</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03010</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-3.7188</td>\n",
              "      <td>393.750</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03012</th>\n",
              "      <td>190.0</td>\n",
              "      <td>4.7500</td>\n",
              "      <td>423.440</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03014</th>\n",
              "      <td>190.0</td>\n",
              "      <td>12.7188</td>\n",
              "      <td>398.440</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03016</th>\n",
              "      <td>190.0</td>\n",
              "      <td>19.1875</td>\n",
              "      <td>323.435</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03018</th>\n",
              "      <td>190.0</td>\n",
              "      <td>24.2812</td>\n",
              "      <td>254.685</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03020</th>\n",
              "      <td>190.0</td>\n",
              "      <td>27.9375</td>\n",
              "      <td>182.815</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03022</th>\n",
              "      <td>190.0</td>\n",
              "      <td>30.4375</td>\n",
              "      <td>125.000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03024</th>\n",
              "      <td>190.0</td>\n",
              "      <td>31.8438</td>\n",
              "      <td>70.315</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03026</th>\n",
              "      <td>190.0</td>\n",
              "      <td>32.2500</td>\n",
              "      <td>20.310</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03386</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-34.6563</td>\n",
              "      <td>34.375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1.03388</th>\n",
              "      <td>190.0</td>\n",
              "      <td>-33.5625</td>\n",
              "      <td>54.690</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         stimulus  response  derivative\n",
              "1.02992     190.0  -38.2188      20.310\n",
              "1.02994     190.0  -37.5313      34.375\n",
              "1.02996     190.0  -36.1250      70.315\n",
              "1.02998     190.0  -33.7500     118.750\n",
              "1.03000     190.0  -30.6875     153.125\n",
              "1.03002     190.0  -27.0625     181.250\n",
              "1.03004     190.0  -23.0938     198.435\n",
              "1.03006     190.0  -18.0312     253.130\n",
              "1.03008     190.0  -11.5938     321.870\n",
              "1.03010     190.0   -3.7188     393.750\n",
              "1.03012     190.0    4.7500     423.440\n",
              "1.03014     190.0   12.7188     398.440\n",
              "1.03016     190.0   19.1875     323.435\n",
              "1.03018     190.0   24.2812     254.685\n",
              "1.03020     190.0   27.9375     182.815\n",
              "1.03022     190.0   30.4375     125.000\n",
              "1.03024     190.0   31.8438      70.315\n",
              "1.03026     190.0   32.2500      20.310\n",
              "1.03386     190.0  -34.6563      34.375\n",
              "1.03388     190.0  -33.5625      54.690"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "metadata": {
        "id": "LUjxQmQ3nBjW",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### 2c) What is the time point when the first spike (action potential) exceeds threshold?  Note that this will be the first time point in the entire response that exceeds threshold.  "
      ]
    },
    {
      "metadata": {
        "id": "_Oom_2hDnBjZ",
        "colab_type": "code",
        "outputId": "069152bb-2f3a-4fed-ab5a-bb0473efc70e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "cell_type": "code",
      "source": [
        "# You can access values from the index of a data frame with .index, \n",
        "# and then access entries from that index numerically (e.g. [7] for the 7th value)\n",
        "t = df.index[9]\n",
        "print(\"The threshold is first crossed at t = %.5g s\" % t)"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The threshold is first crossed at t = 0.00018 s\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "ZEPOz2XonBjd",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### 2d) What is the membrane potential (not the slope) at that threshold?  Write as a print statement with three significant digits.  Don't forget units!"
      ]
    },
    {
      "metadata": {
        "id": "1IQSMeW5nBje",
        "colab_type": "code",
        "outputId": "621da374-3a5a-4d84-fec1-3d5c6af3d2b0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "cell_type": "code",
      "source": [
        "# You can access value in a column by their index, with .loc[]\n",
        "v_at_threshold = 50\n",
        "print(\"the membrane potential at that threshold is t= %.3g\" % t)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "the membrane potential at that threshold is t= 0.00018\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "VxT7rVfcnBjh",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "<hr>"
      ]
    },
    {
      "metadata": {
        "id": "ee6GEl_5nBji",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## 3) "
      ]
    },
    {
      "metadata": {
        "id": "mSy2uIKLnBjj",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### You may have noticed (by eye) in the original membrane potential trace that the first spikes (action potentials) is taller, narrower, and occurs at a slightly lower threshold than the rest, and that the time between spikes increases.  This is called adaptation, and it is something that many neurons do in response to stimuli.  In fact, many neurons are classified as \"adapting\" vs. \"non-adapting\".  \n",
        "\n",
        "#### Many excitatory cells are adapting, while some notable inhibitory cells are non-adapting.  This means that the \"go\" neurons can always be overcome by the \"stop\" neurons, because the \"stop\" neurons are able to  \"fire\" spikes at very high rates without slowing down.  This is a negative feedback mechanism which keeps overall activity in line (e.g. preventing seizures).  "
      ]
    },
    {
      "metadata": {
        "id": "2nPl2fbQnBjk",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### 3a) Neurons are often classified by an \"adapation index\", sometimes defined as the ratio between the 3rd and the 1st \"inter-spike-interval\", or time between spikes.  Using the spike times extracted in question 1, compute the adaptation index for the membrane potential trace that we have been working with.  "
      ]
    },
    {
      "metadata": {
        "id": "Y22OvSzrnBjn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        },
        "outputId": "cf7ec342-67a8-4c28-c769-d7e082c98699"
      },
      "cell_type": "code",
      "source": [
        "# Recall that \"spike_indices\" is just the row numbers in the data frame where the peaks occurred.  \n",
        "# First we compute the spike times by using the dataframe's index, and grabbing only those indices that correspond to spike peaks.  \n",
        "# The .values part here let's us convert to something more intuitive (the values, separated from the dataframe).\n",
        "# Don't forget to put the units on at the end!\n",
        "spike_times = df.index[5].values * 10\n",
        "spike_times"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "error",
          "ename": "AttributeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-43-4adcec0e75a4>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mspike_times\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mspike_times\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mAttributeError\u001b[0m: 'numpy.float64' object has no attribute 'values'"
          ]
        }
      ]
    },
    {
      "metadata": {
        "id": "BKVnzymNnBjr",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# The inter-spike intervals are just the intervals between spikes, i.e. the differences between adjacent spike times.  \n",
        "# Here was can use .diff() and not worry about dt because this is actually just a difference between adjacent numbers, not a derivative.  \n",
        "inter_spike_intervals = np.diff(...)\n",
        "inter_spike_intervals"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "quHxP8TinBjx",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Now compute the ratio of the 3rd of these to the 1st of these.\n",
        "# Don't forget that indices start from 0 in Python (and C, C++, etc.)\n",
        "# Print to three significant figures\n",
        "adapation_index = ...\n",
        "print(...)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "hxqzTewDnBj0",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Write a statement that is `True` if this adaptation index is >1.5, and `False` if it is not.  \n",
        "# You could use such a statement as part of a program to sort neurons into \"adapting\" and \"non-adapting\" categories.\n",
        "..."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "jPMru4gonBj4",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### 3b) The spikes also get wider. This happens because, after the first spike, not all of the ion channels are ready to participate in the generation of the next spike (some have become inactivated).  This means that the upstroke of the action potential is a bit less vigorous (as is the downstroke, mediating by potassium channels). In milliseconds, how much wider is the second spike than the first?  "
      ]
    },
    {
      "metadata": {
        "id": "1bQXST_NnBj6",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# First we have to figure out the width of one spike.  \n",
        "# The width is often defined as the time when the membrane potential crosses above the threshold (from question #2) \n",
        "# at spike onset until the time when it crosses below it at the end of the spike.  \n",
        "# Let's give ourselves some runway and extract a period of time +/- 50 samples of the first spike's peak.\n",
        "# Recall that spike_indices contains the locations of the samples for each spike's peak.  \n",
        "first_spike_index = ...\n",
        "\n",
        "# .loc[] is great for finding a location by name in the index.  But the names in our index are time values, and we have indices here.  \n",
        "# Use .iloc[] (the \"i\" stands for integer) to access by index.  \n",
        "first_spike_data = df[...].iloc[...]\n",
        "\n",
        "# But we don't just want that exact sample.  We want +/- 50 samples around the spike.  \n",
        "# You can get a \"slice\" of the dataframe using a range like .iloc[first:last], where first and last are some values of your choosing.  \n",
        "first_spike_data_range = ...\n",
        "\n",
        "# If all went well, this should like like a plot of the first spike\n",
        "first_spike_data_range.plot()\n",
        "plt.xlabel('Time (s)')\n",
        "plt.ylabel('Membrane\\nPotential (mV)');"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "2T2idcFJnBj8",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Now you need to extract only those values that are above the threshold determined in question #2d.  \n",
        "# Use a selector to extract only the values in first_spike_data_range that are above that threshold.  \n",
        "# Note that the threshold is not the value of the red line (which is a threshold for the first derivative), \n",
        "# But the actual threshold you got in question #2d.  \n",
        "is_first_spike_above_threshold = ... > ...\n",
        "first_spike_above_threshold = first_spike_data_range[...]\n",
        "first_spike_above_threshold.head()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "_yauYTk1nBkA",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Now you need to find the difference between the first and last time point in `first_spike_above_threshold`\n",
        "# This will be the width of the spike.  \n",
        "# You probably know by now how to access the first element of an array.  \n",
        "# You can access the last element of an array in several ways, but the coolest is with [-1].  \n",
        "# Why does the index -1 work?  Imagine that the array was wrapped onto a circle.  If 0 is the first element, than -1 is the last element!\n",
        "# Don't forget to use .index to access the times (not the membrane potential values), and don't forget to use units!\n",
        "first_spike_width = (... - ...) * ...\n",
        "\n",
        "# Report the width in ms to three significant figures.\n",
        "print(...)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "kekb_VtTnBkD",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Finally, you will need to repeat this for the second spike.  \n",
        "# Note that you will need to obtain the threshold again as you did in question #2, but this time for the second spike instead of the first.\n",
        "# Hint: at t = 1.032 seconds, the first spike is over and the second spike hasn't begun yet.  You can use this value to extract data for\n",
        "# only the second spike and beyond, and then repeat the strategy from question #2 to extract it's threshold.  \n",
        "df_no_first_spike = df[df.index > ...]\n",
        "is_slope_greater_than_threshold = ...\n",
        "places_where_slope_is_greater_than_threshold = ...\n",
        "t = ...\n",
        "v_at_threshold = ...\n",
        "second_spike_index = spike_indices[...]\n",
        "second_spike_data = ...\n",
        "second_spike_data_range = ...\n",
        "\n",
        "# Plotting is optional\n",
        "second_spike_data_range.plot()\n",
        "plt.xlabel('Time (s)')\n",
        "plt.ylabel('Membrane\\nPotential (mV)');\n",
        "\n",
        "is_second_spike_above_threshold = ...\n",
        "second_spike_above_threshold = ...\n",
        "second_spike_width = ... # Use this line to compute the value\n",
        "second_spike_width = ... # Use this line to rescale to milliseconds\n",
        "spike_width_difference = ... - ...\n",
        "print(\"The seconds spike is ... wider than the first\" % ...)"
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}